Jones H. — Theory of Brillouin Zones and Electronic States in Crystals :: Электронная библиотека попечительского совета мехмата МГУ

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Jones H. — Theory of Brillouin Zones and Electronic States in Crystals

Jones H. — Theory of Brillouin Zones and Electronic States in Crystals

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Название: Theory of Brillouin Zones and Electronic States in Crystals

Автор: Jones H.

Аннотация:

This book is written for students of theoretical solidstate physics, and for experimental physicists who have an interest in the study of electronic states in crystals. The presentation emphasises those aspects of the theory which are of general validity and the mathematical methods employed arc applicable to any crystal-lographic type. The treatment does not assume an extensive knowledge of mathematics. To help the reader, for example, the equations required for the construction of character tables are derived in the text from a few basic theorems. The examples used to illustrate the spectra of electronic states in crystals are chosen for their practical importance rather than for convenience of form. The representation of electronic states in extended wave-vector space is discussed and methods are given for the reduction of this space to the fundamental Brillouin zone. This representation is applied to the electron theory of alloys. Spin-orbit fine structure in semi-conductors and the properties of the double group are considered in the final chapter.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1960

Количество страниц: 268

Добавлена в каталог: 18.08.2009

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Предметный указатель

A-matrices      30
A-matrices for close-packed-hexagonal      137
A-matrices, for body-centred-cubic      31
A-matrices, for face-centred-cubic      31
A-matrices, for rhombohedral      55
A-matrices, fora-uranium      160
Abelian groups      20 32
Accidental degeneracy      10
Alkali metals      60
Alloy phases      205
ALTMAN, S.L.      172
Angle between primitive vectors      31
ASENDORF, R.H.      172
Atomic orbitals, superposition of      225
B-matrices      33
B-matrices for $\alpha$ -uranium      160
B-matrices for body-centred-cubic      33
B-matrices for face-centred-cubic      155
B-matrices for rhombohedral      56
B-matrices, for close-packed-hexagonal      137
Bands, touching and overlapping      45
Bardeen, J.      245
Basis functions      92
BELL, D.G.      172
Bethe, H.      28 125
BETTERTON, J.P.      214
Bismuth      57 197
Bloch wave functions      34
Bloch wave functions degenerate      79
Bloch, F.      28
Bonding functions      140 151
BOUCHAERT, L.P.      28
boundary conditions      9 17
Bradley, A.J.      214
Bragg reflections, law of      38
Brass- $\beta$       103
Brass- $\gamma$ , large zone for      207
Brass- $\gamma$ , space group of      207
Brass- $\gamma$ , wave-vector groups of      210
Bravais lattices      29 30
Brillouin zones, continuity of $\varepsilon(\kappa)$ in      39 42
Brillouin zones, for $\alpha$ -uranium      161
Brillouin zones, for bismuth      198
Brillouin zones, for cubic metals      103 117 121
Brillouin zones, for rhombohedral metals      57
Brillouin zones, symmetry points of      101 117 121
Brillouin zones, symmetry within      38
Brillouin, L.      28 214
Brooks, H.      245
Callaway, J.      172
Cellular method      233
Cellular method, boundary conditions for      235
Cellular method, eigenvalue by surface integral      241
Cesium chloride, Brillouin zone of      170
Cesium chloride, structure of      60 103
Chambers, R.G.      59
Character tables of double group      254 257 258 260
Character tables of point groups $\bar{3}m$       95
Character tables of point groups $\bar{6}m2$       101
Character tables of point groups $\frac{4}{m}mm$       99
Character tables of point groups 6mm      86
Character tables of point groups m3m      90
Character tables of point groups mmm      97
Character tables of wave vector groups      107 118 122 123 139 141 142 164 167 172
Character tables, calculation of      80
Chodorow, M.I.      59
Classes, determination of      74
Classes, multiplication of      75
Classification of states      101
Close-packed-hexagonal structure      60
Close-packed-hexagonal structure, group of $\Sigma$       142
Close-packed-hexagonal structure, groups of, A and $\Gamma$       138
Close-packed-hexagonal structure, groups of, M and L      141
Column vector      21 77
Commutation rule      133
Compatibility relations      108
Compatibility relations with respect to symmetry planes      110
Conduction band      43
Connectivity of Fermi surface      49 54
Cubic lattice, body-centred      31
Cubic lattice, Face-centred      31
Cubic lattice, simple      30
De Haas van Alphen effect      54
Degeneracy, removal of in second order      183
Density of states      49
Density of states for $\gamma$ -brass      212
Density of states, discontinuity in derivative of      52
Diagonal      130 148
Diagonal glide reflections      148
Diamond structure      148
Diamond structure, degeneracy at X      152
Dirac $\delta$ -function      12
Direction-ratios      67
Distance between reflecting planes      34
Double group      246 250
Double group, character tables of      253 254 257 258
Double group, classes of      251
Dresselhaus, G.      263
Drude — Lorentz electron theory      1
Drude, P.      28
effective mass      16
Effective reciprocal mass tensor      42
Eigenvalue spectrum      14
Electronic specific heat      54
Electronic specific heat of $\alpha$ -brasses      216
Elliott, R.J.      263
Empty lattice test      241
Energy bands for free electrons      111 118
Energy bands of germanium and silicon      196
Energy bands, based on atomic p-states      220
Energy bands, based on atomic s-states      219
Energy bands, touching and overlapping      44
Energy discontinuity, planes of      182
Enumeration of states      17
Equi-energy surfaces      46
Equivalent axes and planes      75
Eulerian angles      249
Extended k-space      173
Factor group      126
Fermi surface      43
Fermi surface in orthorhombic lattices      48
Fermi surface, the connectivity of      52
Fermi — Dirac statistics      3
Fletcher, G.C.      59
Free electron energy bands      111
Free electron energy bands for $\alpha$ -uranium      168
Free electron energy bands for body-centred cubic lattices      116
Free electron energy bands for close-packed hexagonal lattices      145
Free electron energy bands for face-centred cubic lattices      124
Free electron energy bands for simple cubic lattices      112
Glide reflections      126
Glide reflections, simple      129
groups      60
Groups of wave-vectors      102
Groups of wave-vectors at $\Delta$ -points      105 158 167
Groups of wave-vectors at $\Gamma$ -points      90 et seq. 139 164 253 254
Groups of wave-vectors at $\Lambda$ -points      107 258
Groups of wave-vectors at $\Sigma$ -points      107 142
Groups of wave-vectors at A-points      138
Groups of wave-vectors at L-points      121 141
Groups of wave-vectors at M-points      103 141 154
Groups of wave-vectors at N-points      118
Groups of wave-vectors at P-points      118
Groups of wave-vectors at W-points      123
Groups of wave-vectors at X-points      103 154
Groups of wave-vectors at Z-points      107
Groups, multiplication table of      72
Groups, representations of      76
Hamiltonian with spin-orbit term      247

Hamiltonian, matrix elements of      41
Herman, F.      125 172
Hermann — Manguin notation, for point groups      70
Hermann — Manguin notation, for space groups      127 131
Herring, C.      59 172 263
Hexagonal system      99
Hexagonal system, Herring's notation for classes in      138
HIGMAN, B.      172
Howarth, D.J.      245
Hume-Rothery, W.      205 214
Indium-antimonide      246
Integral vectors      65
Invariant subgroups      132
Irreducible representations      78
Jones, H.      28 59 214 245
Kane, E.O.      263
Kip, A.F.      263
Kittel, C.      263
Kohn, W.      59 245
Kramers' treatment of one-dimensional case      18
Kramers, H.A.      28
Kronig and Penney model      11
Kronig, R. de L.      28
Krutter, H.M.      59
LACO method, difficulties of      228
Large zones      173
Large zones of alloy phases      205
Large zones of bismuth structure      198
Large zones of diamond structure      193
Large zones of hexagonal close packed structure      191
Large zones, complete and incomplete      174
Large zones, geometry of      206
LCAO Method      216
Lorentz, H.A.      28
magnetic susceptibility      54
Magneto-resistance effect      54
Manning, M.F.      59
MARITA, A.      214
Matrices, trace of      65
Matrix elements, of Hamiltonian      181
Miller indices      34 45
Mott, N.F.      216 245
Nearly free electron approximation      180
Noble metals      60
NUTKINS, M.A.E.      59
One-dimensional energy bands      25
Opechowski, W.      263
Optical properties      216
Orthogonal transformations      38
Orthogonality relations      83
Orthogonalized plane wave method      229
Orthogonalized plane wave method, difficulties of      232
Orthorhombic lattice      76
PARMINTER, R.M.      263
Pauli spin matrices      247
Pauling's theory of covalent bond      204
Peierls, R.      28 214
Penney, W.G.      24
Phillips, F.C.      88 125
Phillips, J.C.      125
Pippard, A.B.      216 245
Point groups      38 60
Point groups containing the inversion      86
Point groups, $\bar{3}m$       95
Point groups, $\bar{4}3m$       92
Point groups, $\frac{3}{m}mm$ , $\bar{6}m2$       99
Point groups, $\frac{4}{m}mm$       98
Point groups, 3m      94
Point groups, holosymmetric      65
Point groups, mmm      96
Point groups, operations of      61
Point groups, operators of expressed as substitutions      90
Point groups, particular      432
Potential energy, in variance of      31
Primitive translation      29
RAYNE, J.A.      245
Reality of V(x), effect of      28
Reciprocal effective masses      42 183
Reciprocal lattice      32
Reduction of k-space      187
Reduction of k-space, rules for      188
Regular permutations      77
Regular representations      76
Regular representations, reduction of      78
Reitz, J.R.      214
Rhombohedral lattices      55
Rhombohedral lattices,Brillouin zones for      57
ROSTER, G.F.      59 125
Schiff, B.      172
Schiff, L.I.      263
Schroedinger equation      4
Screw-displacements      29 60 126
Screw-displacements, diad and triad      128
Seitz, F.      28 125
Self-consistent field      111
Shockley, W.      245
Similarity transformation      21 79
Single-electron model      2
Slater, J.C.      172 245
Space groups      60
Space groups, details of Cmcm      159
Space groups, details of Fd3m      148
Space groups, details of P $\frac{63}{m}mс$       135
Space groups, notation for      127
SPEIZER, A.      125
Spin-orbit coupling      246
Spin-orbit effect at arbitrary k      262
Spin-orbit fine structure      254
Spin-orbit fine structure along axes from $\Gamma$       261
Stereographic projection      66
Stereographic projection for zone construction      208
Structure factor      186
Structures, $\alpha$ -uranium      159
Structures, close-packed hexagonal      135
Structures, cubic      30
Structures, diamond      148
Structures, rhombohedral      55
Strutt, M.J.O.      28
Suffczynski, M.      216 245
Symmetry types      92
Tetragonal system      98
Thermoelectric power      54
Thewlis, J.      214
Tight-binding approximation      96 216
Tight-binding approximation, difficulties of      228
Tight-binding approximation, mixing of s and p atomic orbitals      227
Time reversal symmetry      262
Transition metals, Mott's theory of      216
Translation group      29 60
Translation lattice      30
Transposed matrix      64
Trigonal system      95
Unit polyhedron      37
Uranium, $\alpha$ -      159
Uranium, $\alpha$ -, Brillouin zone for      161
Uranium, $\alpha$ -, character tables for      164 167
Uranium, $\alpha$ -, free electron energy bands of      168
Uranium, $\alpha$ -, symmetrized free electron wave functions for      166
Valence band      43
Variation principle      231
VON DER LAGE, F.C.      28
Wave-vector group      131
Wave-vectors, representation on torus      36
Wigner, E.      28 125 263
Wilson, A.H.      28
WOODRUFF, T.O.      245
wronskian      5 20
Zinc-blende structure      252
Zones, large      173
Zones, large, complete and incomplete      174 190

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